Hamilton-Jacobi approach for Regge-Teitelboim cosmology

Abstract

The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to obtaining the Hamilton principal function $S$. In order to do this, we avoid the second-order in derivative nature of the model by appropriately defining a set of auxiliary variables that yields a first-order Lagrangian. Being a linear in acceleration theory, this scheme unavoidably needs an adequate redefinition of the so-called Generalized Poisson Bracket in order to achieve the right evolution in the reduced phase space. Further this Hamilton-Jacobi framework also enables us to explore the quantum behaviour under a semi-classical approximation of the model. A comparison with the Ostrogradski-Hamilton method for constrained systems is also provided in detail.

22 pages, no figures

References in corpus (4)

• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Hamilton-Jacobi Approach for First Order Actions and Theories with Higher Derivatives
• Involutive constrained systems and Hamilton-Jacobi formalism
• Gauge symmetry and Virasoro algebra in quantum charged rigid membrane -- a first order formalism

Cited by in corpus (1)

• Dark matter as a gravitational effect in the embedding theory approach